Question

A sculpture is in the shape of a square pyramid. The sculpture has a height of 36 feet and a volume of 19,200 cubic feet. Find the side length of the square base

Answer 1

40ft

Explanation:

The volume of a square pyramid is given by:

`V=(l^2h)/(3)`

where V is the volume, l is the length of the square base, and h is the height.

Since we need to find the length, we solve for
`l` in the last equation:

`l^2h=3V\\\\l^2=(3V)/(h) \\\\l=\sqrt{(3V)/(h) }`

and now, we substitute the known values:

`V=19,200ft^3\\h=36ft`

and we get the following:

`l=\sqrt{(3(19,200ft^3))/(36ft) }\\ \\l=40ft`

the length of the square base is 40ft